Short guide to understanding spatial resolution, noise level, and radiometric resolution By Davide Castelletti & Gordon Farquharson
The number and variety of applications that exploit Synthetic Aperture Radar (SAR) data are growing. These applications include environmental monitoring, surveillance, emergency response, infrastructure monitoring, urban planning, and food security. With the growing demand for SAR images, the community of SAR users is also transforming. Radar images are now processed by GIS users, software developers, and computer vision and machine learning engineers, and are increasingly interpreted by non-radar specialists.
In this article, we describe key characteristics of SAR imagery, with the goal of providing a short guide to understanding SAR products. We present the aspects of spatial resolution that are particular to SAR, and cover concepts such as noise level and radiometric resolution that are related to radar design and image formation. We will see that resolution is not the only parameter one should consider when evaluating SAR image quality, but instead that a set of different parameters should be assessed collectively to select the best data for each specific application.
SAR acquisition geometry
In contrast to optical imagers, synthetic aperture radar systems only acquire imagery from the side of the scene (Figure 1). A SAR image is formed from data collected by a coherent radar that transmits pulses of radio frequency energy toward the ground and measures the strength of the reflected signal as a function of distance (“time of flight”) from the radar. In addition, the platform carries the SAR antenna along a track, and by this action, the ground is “scanned” in two dimensions. In the ranging (“range”) dimension, objects are placed according to their distance from the radar. The second dimension is the “along-track” (or “cross-range” or “azimuth”) dimension. In this dimension, the ground is scanned by the beam moving across the ground at a rate equal to the speed of the platform, and objects are placed in this dimension according to their position along the track. An image is built up from the reflected signals in both dimensions. As a result of this acquisition methodology, the resolution of a SAR image has two components: a range resolution and an azimuth resolution.
Spatial resolution: range and azimuth resolution
As outlined above, a SAR image has two dimensions, range and azimuth. The resolution in these dimensions is achieved using different aspects of the signal recorded by the radar, and as a result, the resolution in the range direction can (and most often is) different to that in the azimuth direction.
The spatial resolution of SAR data is defined by the impulse response (IPR). The IPR of a SAR system is the response of the sensor and processing to a theorectical spatial impulse target, i.e., a target that is infinitesimally small in all dimensions. IPR is a two-dimensional entity that is characterized by the range-dimension width (the width of the IPR in the ranging dimension) and the cross-range (or azimuth) dimension width. The generally-accepted definition of radar resolution is the width of the IPR at points at 3 dB below the peak of the IPR. In the range dimension, a larger transmitted bandwidth corresponds to improved range resolution. In the cross-range dimension, a larger Doppler bandwidth corresponds to better azimuth resolution. IPR is also affected by the processing used to form the image, e.g., windowing, and distortions in the signals due to hardware limitations or uncompensated platform motion.
Unless specified, IPR, and thus inherent SAR sensor resolution, is defined in the slant-range plane. When the SAR image is translated to the ground plane, the mapping from slant range to ground range causes the IPR to broaden (Figure 1b). Therefore, the IPR-defined range resolution in the ground plane is always worse than that in the slant plane. Resolution in the cross-range direction does not change in the slant plane to ground plane mapping.
The ground-range resolution (resolution in the ranging direction in the ground plane) depends on the bandwidth of the transmitted signal and the angle from which the ground is imaged (look angle). Larger bandwidth enables a better range resolution. For instance, the theoretical resolution with a 300 MHz bandwidth is 0.5 m in the slant plane and 0.91 m in the ground plane at a look angle of 30 degrees. With a bandwidth of 500 MHz, the slant range resolution is 0.3 m and the ground-range resolution is 0.55 m for the same look angle.
As mentioned, the azimuth resolution depends on the Doppler bandwidth. A larger Doppler bandwidth can be obtained by pointing the antenna beam at a target for a longer time. Many existing SAR satellites use phased array antennas to steer the beam to dwell on objects. As these phased array antennas are designed to scan over a few degrees, the azimuth resolution achieved is on the order of tens of centimeters.
Capella SAR satellites have a transmitter bandwidth of 500 MHz, so can achieve 0.3 m resolution in the slant plane. The satellites have also been designed to point to a spot on the ground for tens of seconds, thereby achieving centimeter-scale azimuth resolution. This fine resolution is used to reduce speckle in the images (see section below) and provide high-quality multi-looked SAR imagery. An example of high-resolution multi-looked Capella imagery is shown in Figure 2.
Noise level and image quality
In addition to spatial resolution, other metrics are important in overall interpretability of a SAR image. The radar measures the intensity of the reflected signal at each resolution cell in the image. The intensity depends on the transmitted power, antenna gain, distance between the scatterer and the radar, and geometry, roughness, and material properties of the object being imaged. For interpreting intensity in a radar image, two features are important: the ability to make out objects against the inherent noise generated by the sensor, and the ability to discriminate two objects that have similar intensities. The first is captured by the noise equivalent sigma zero (NESZ) of a SAR image. The second is captured by the concept of radiometric resolution.
A target is detectable in a SAR image when, for a certain pixel resolution, the received power and therefore the intensity at the pixel level overcomes the thermal noise that the system electronics generate. In SAR, NESZ is the most commonly used metric that captures the effect of system noise on image quality. It can be analytically predicted during the design of the radar and can be empirically measured over “dark” targets in the SAR image. For instance, calm lakes are highly reflective targets in the side-looking geometry and allow the characterization of the noise level of the sensor.
The effect of NESZ on image interpretability is demonstrated with the images in Figure 3. The SAR data were processed to 0.5 m ground range resolution and 0.5 m azimuth resolution. In both cases, bright scatterers, e.g., buildings, are clearly detectable. The difference between the two is the NESZ (–10 dB versus –20 dB). The aircraft and the roads are far more discernible in the image that has an NESZ of –20 dB. In particular, the aircraft shadows are much clearer in the –20 dB NESZ image. This shows that lower NESZ values are preferable when targets with low-backscattering intensity need to be detected.
NESZ varies also with transmitted bandwidth (range resolution). A SAR image generated with a 300 MHz transmitted bandwidth (0.5 m slant-range resolution) will have more noise than one generated with 150 MHz (1 m slant-range resolution). A wider bandwidth enables better resolution, but causes more noise in imagery (higher NESZ).
Speckle, radiometric resolution, and target detection & identification
Speckle is caused by the reflection of the radar signal from multiple objects (scatterers) that are distributed within a resolution cell. The branches and leaves of a tree, grass and rocks in a field, and bricks that make up the walls of a building are examples of objects that have distributed scatterers. The sum of the contribution from all the scatterers results in variation in the intensity of the measured signal in adjacent resolution cells. This variability in image intensity, called speckle, limits the radiometric resolution of a SAR sensor.
Speckle in images looks like the snowy noise found on old analog television sets. Speckle makes it harder to distinguish features in SAR images because it corrupts the outline of objects. Radiometric resolution is a metric that describes the ability of a sensor to discriminate between two objects that have similar radar cross sections (i.e., that are radiometrically similar). Radiometric resolution depends on the measured signal to noise ratio and the number of independent looks from which the pixel was formed. Overcoming speckle and improving radiometric resolution is only possible by averaging multiple SAR images or averaging pixels in a SAR image. This averaging process is commonly referred to as “multi-looking”.
Multi-looking in single SAR images is most typically done by averaging adjacent pixels. Sometimes this averaging is achieved using sophisticated techniques, but the result is always a loss of resolution compared to the original image. For example, a 4-look 1 m (slant range resolution) × 1 m (azimuth resolution) spotlight image could be created from a SAR acquisition that has a slant range-resolution of 1 m and an azimuth resolution of 0.25 m, by averaging 4 adjacent 0.25 m resolution cells to form a 1 m cell in the azimuth direction.
Multi-looking is a common pre-processing step for SAR users interested in change detection or in target detection or classification. We demonstrate the image quality improvement using multi-looking with Capella data. The images in the left column of Figure 4 are from a low-resolution SAR imaging mode that has been multi-looked to reduce speckle and improve radiometric resolution. The boxed sections of the image have been reproduced below to show that the loss of spatial resolution significantly hinders identification of objects in the scene. The images in the middle column are single-look 0.5 m resolution images (both azimuth and ground range) where the speckle in the image hinders the identification of small targets. The image in the third column is a multi-looked 0.5 m resolution image. The shadow of the aircraft is significantly improved, and the features on the grassy areas are clearly visible.
In SAR, a few key metrics define the performance of the system. First, and not surprisingly, resolution is an important measure. Sub-meter resolution is considered a “must have”, but as demonstrated in this article, image interpretation is a function of spatial resolution, NESZ, speckle, and radiometric resolution. Low-NESZ imagery is desirable because objects that scatter radar signals weakly are visible in low-NESZ SAR images, but high resolution and low NESZ are not the only factors that influence interpretation and detection in SAR images. Speckle makes it harder to distinguish features in SAR images because it reduces the contrast between objects. Thus, the interpretability of SAR images is determined by a complex mix of resolution, NESZ, and multi-looking. These factors are critical but are often overlooked in common discourse surrounding SAR. Novice and expert SAR users should consider all of these parameters when selecting SAR imagery for their application.
- Note that for simplicity, we will restrict this discussion to side-looking SAR systems, and not deal with squinted-SAR systems in this post.
- For more details of SAR processing, please see A. Moreira, P. Prats-Iraola, M. Younis, G. Krieger, I. Hajnsek and K. P. Papathanassiou, “A tutorial on synthetic aperture radar,” in IEEE Geoscience and Remote Sensing Magazine, vol. 1, no. 1, pp. 6-43, March 2013.
- “Anatomy of a SAR Impulse Response” from Sandia National Laboratories.
- Note that for squinted SAR, things are a little different, because the ranging and cross-ranging directions are not orthogonal to one another.
- For spaceborne systems, the difference between look angle and incidence angle matters because of the curvature of the earth.